Information on Result #599880
There is no digital (6, 51, 86)-net over F9, because extracting embedded orthogonal array would yield linear OA(951, 86, F9, 45) (dual of [86, 35, 46]-code), but
- construction Y1 [i] would yield
- linear OA(950, 55, F9, 45) (dual of [55, 5, 46]-code), but
- construction Y1 [i] would yield
- OA(949, 51, S9, 45), but
- the (dual) Plotkin bound shows that M ≥ 1 546132 562196 033993 109383 389296 863818 106322 566003 / 23 > 949 [i]
- OA(95, 55, S9, 4), but
- discarding factors would yield OA(95, 44, S9, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 60897 > 95 [i]
- discarding factors would yield OA(95, 44, S9, 4), but
- OA(949, 51, S9, 45), but
- construction Y1 [i] would yield
- OA(935, 86, S9, 31), but
- discarding factors would yield OA(935, 85, S9, 31), but
- the linear programming bound shows that M ≥ 112620 123087 737061 231244 499443 215625 747636 066957 184847 246285 / 44 721454 781644 057928 595589 > 935 [i]
- discarding factors would yield OA(935, 85, S9, 31), but
- linear OA(950, 55, F9, 45) (dual of [55, 5, 46]-code), but
Mode: Bound (linear).
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No digital (6, 52, 86)-net over F9 | [i] | m-Reduction | |
| 2 | No digital (6, 53, 86)-net over F9 | [i] | ||